Capacity of batteries is measured by Amp Hours, and it's unfortunately unlikely that you've got a 1000AH battery. More likely you've got something around the 100 AH range, unless you and 15 professional wrestlers carried it to your car.
Look for a 20 hour capacity rating on the housing of the battery. Also look for what type of battery it is (although for $50, it's likely a flooded battery, probably sealed - other possibilities would be AGM or gel cell.)
I think your setup will do what you want it to, although you'll probably need a trickle charger to keep the battery in good shape. You can get one cheap, and leave it attached to the battery. Without a charger, a flooded battery discharges all by itself quickly enough that over the course of a few months it will lose some charge. And when it sits partially discharged for long periods it can permanently lose some of it's capacity, so you'll want to keep it topped off. (AGM batteries have much lower rates of self-discharge, and may not require a charger)
Your system won't be automatic the way a UPS is, so you'd need to be around when the power goes out to plug your powerheads into the inverter. You could probably set up a relay to act as an automatic transfer switch, but that's beyond me. One of the electrical engineers on here can give you advice on that.
I'd skip the return pump, because your skimmer isn't running anyways, so there's no point of moving all that water through your sump. The return pump uses a lot of electricity, so in the interest of run-time, you'd be much better off just running the powerheads, since it's most important to keep the water in the tank moving, and aerated. (point one of those powerheads up towards the surface!)
To figure out how long your backup battery will run, you need to know the capacity of the battery, and the wattage of your load.
Lets assume your battery is 100 Ah at 12 Volts, and your powerheads are 10 watts each. To figure out the 12V current draw of those powerheads (since your battery is 12V) you divide 20 watts by 12 volts (because P=IV, so I=P/V). So the current draw of the powerheads is 1.7 amps at 12 volts.
If your battery is rated at 100Ah, about half of that capacity is usable without damaging the battery, and before you might drop below the input voltage of your inverter. This is a ballpark thing depending on some factors not clear in this thread, and also assuming that you care about the number of discharge cycles you'll get out of this battery (which you may not because it was cheap, and it's for emergencies). But we'll assume 50Ah usable capacity. Divide that by the 1.7 A that the powerheads are drawing to get the number of hours until you've drawn 50 Ah. The result is 30 hours.
Let's say the mak4 draws something like 100 watts (I think that's close), which is 8.3 amps at 12v. With the powerheads that's a total load of 10 amps, so you'd get about 5 hours running everything. In reality the time would be shorter than 5 hours, because when batteries are discharged quickly their capacity is lower. (that's why the Ah rating is given with a time period, like 20 hours. At 5 hours the Ah rating is quite a bit lower).
So there's all you never wanted to know about lead-acid batteries!